## Cost of Capital May Change

The cost of capital in an emerging market valuation may change based on evolving inflation expectations (embedded in the risk-free rate and cost of debt), shifts in the openness of the economy, and expected market volatility. There are two ways of incorporating them in the cost of capital: Calculate a year-by-year cost of capital using different assumptions for each period (recommended for high inflation, highly volatile, or restricted countries) or compound the changes and incorporate them as a single addition to the cost of equity and debt to derive one cost of capital for the whole period. The first approach is much more accurate.

Whatever Method You Choose to Calculate the Cost of Capital—Be Consistent with How the Cash Flow is Estimated

If you are using local nominal cash flows, the cost of capital must reflect the local inflation rate that is embedded in the cash flows. For real cash flows, inflation must be subtracted from the nominal cost of capital. If you are using probability-weighted scenarios, do not double count risk by including a country-risk premium in the cost of capital.

Estimating the Cost of Equity

This section summarizes how to estimate the components of the cost of equity using the standard CAPM model described in Chapter 10. Risk-Free Rate

In emerging markets, the risk-free rate is not as simple to estimate as it is in developed markets. There are three main problems in determining an appropriate local risk-free rate in emerging markets: Most of the government debt in emerging markets is not, in fact, risk free. The ratings on much of this debt are often well below investment grade. It is difficult to find debt longer than three years in many emerging markets. Finally, the long-term debt that does exist is usually in U.S. dollars, a European currency, or Japanese yen and so is not appropriate to discount local nominal cash flows.

To overcome these obstacles, we recommend a building block approach. Exhibit 19.9 defines three main ways to assemble an emerging market risk-free rate. We make the assumption that cash flows are denominated in local currency.

Exhibit 19.9 Calculating the Risk-Free Rate

The choice of method depends on which bond instrument is available and liquid. If all instruments are available, it is useful to calculate all three methods to develop an estimate of the risk-free rate. Let's start with some definitions.

• Local bondyield. Yield to maturity on a long maturity bond denominated in local currency.

• Credit-risk premium. Additional yield demanded by investors to invest in government bonds with lower than AAA rating to cover the risk of default and credit deterioration.

• Duration differential. The change in yield between bonds of different maturity.

• Sovereign-risk premium. Difference between the yields of a local government bond denominated in U.S. dollars and the equivalent maturity U.S. government bond; includes both country risk and credit risk.

• Inflation differential. The compounded difference between the local inflation rate and the U.S. inflation rate over 10 years.

In method one, the starting point is to select the longest maturity local currency denominated debt available and estimate the yield to maturity.5 The next step is to subtract the sovereign-risk premium, which is the difference between the yield on an international currency-denominated bond like a Brady Bond and its equivalent maturity government bond in the United States or the European Union (EU). The sovereign-risk premium needs to be subtracted because it reflects credit risk and other items that are not part of a risk-free rate. The final step is to adjust the bond so that it is equivalent to a 10-year bond. Usually you can extend the duration by compounding the inflation. In many emerging markets, however, the inflation rates are higher in the early years. As a result, the yield curve is inverted, with the yield declining as the maturity lengthens.

In method two, start with an international currency denominated bond of long duration, and estimate the stripped yield. Then subtract the sovereign-risk premium. If using cash flows denominated in local nominal currency, account for local inflation in the risk-free rate. The international currency bond already has the international currency inflation rate embedded in it, so just add the difference between the international inflation rate and the local rate. You can do this by adding the inflation difference

5 Some emerging markets' country debt is partially guaranteed by international institutions or backed by U.S. Treasury bonds. For these bonds, you need to estimate the yield on the non-guaranteed part of the bond, the ''stripped" yield. Stripped yields are available from bond data suppliers.

year by year to develop a separate estimate of the cost of capital by year. You can also compound the inflation difference between the countries and add it as a single number to calculate a single cost of capital for all periods. The level of inflation difference dictates the choice of methods. If it is high, an annual estimate of the cost of capital is preferable.

Method three is the simplest and is available as an option in all countries. It starts with the 10-year U.S. government yield and adds an inflation differential between the U.S. and the local rate to develop a local nominal risk-free rate.

The key assumption in the calculation of the risk-free rate is that most investors, including investors in local markets, have access to an international risk-free rate. In countries such as India or China, however, local investors do not have access to a global risk-free rate. The most risk-free instrument available to them is the local government debt, which has sovereign risk embedded in the yield. This difference in access to a risk-free rate means that foreign investors will have a lower cost of capital than local investors, at least in the short run. As capital controls ease, this difference should disappear. Determining the timing of this is subjective and should be included as part of a scenario.

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